A sub-optimal feedback control to stabilize a quadrotor vehicle is introduced in this paper. The approach makes use of the passivity property and the dynamic programming theory. The control design is based on the proposition of a Lyapunov function which has been defined as the energetic function for the system and, at the same time, is an approximation of the Bellman function associated with the optimal problem for nonlinear systems. To validate the control strategy, various simulations have been carried out